General manager Brian Cashman visited with Cliff Lee yesterday in the free agent’s Arkansas home but didn’t bring the Yankees’ biggest weapon: the Steinbrenner family checkbook.

Cashman spent several hours with Lee, Lee’s wife Kristen and agent Darek Braunecker, but no financial offers were exchanged, according to a source familiar with the situation.

Instead, Braunecker offered an open invitation for Lee to go to New York or for Cashman to return Arkansas to meet, and Cashman saw the value of face time and a personal touch within a negotiation that is not expected to wrap up quickly. It is believed the Yankees were the first team granted such a visit.

The Yankees, in fact, believe Lee will not make a decision before the Winter Meetings, which run Dec. 6-9 in Orlando.

The deciding issue between the Yankees and Rangers could be how many years it will take to secure Lee, a 32-year-old lefty whom the Yankees have targeted as the top free agent from outside the organization.

Lee is three years older now than CC Sabathia was after the 2008 season, so the Yankees will fight not to give the same seven years that they gave to their current ace, who still has the pitching record total of a $161 million contract.

But the Yankees’ need for a top-of-the-rotation starter is great enough that they probably will blink at some point and go to a fifth or even a sixth year to complete a contract, likely at around the $23 million that Sabathia averages on his deal.

Would the Rangers go that far? They have had an infusion of dollars from new ownership and a new TV deal, plus they have seen what Lee meant to their team since acquiring him in July from Seattle for a package headlined by top prospect Justin Smoak. Nevertheless, perhaps only the Yankees can tolerate the risk of giving a thirty-something pitcher such a long contract.

The Yankees understand the gamble involved in signing a pitcher who turns 33 in late August to a five- or six-year deal.

Lee, however, never has had arm trouble because of pitching mechanics an NL executive called “almost perfect.”

Through two seasons, Sabathia has not disappointed. He is 40-15 and helped the Yankees win a World Series in 2009. He did undergo minor right knee surgery recently.

The same can’t be said for Johan Santana. He signed a six-year deal with the Mets worth $137.5 million and has undergone surgery once in each of the last three years. Mike Hampton? His eight-year, $121 million with the Rockies is the best argument for not giving pitchers long-term deals; with Kevin Brown (seven years, $105 million with the Dodgers) in the conversation.

Lee’s three career stints on the disabled list were caused by abdominal muscle problems. He opened last year on the DL and missed the first two weeks after colliding with a runner at home plate in a spring training game.

“His mechanics lessen the risk of an arm injury, and the arm hasn’t been a problem,” the pitching guru said.

Yet, another pitching evaluator took a realistic approach to giving a hurler a long contract.

“You give them six [years] and hope he pitches four for you,” the scout said. “Lee has good mechanics, but nobody had better mechanics that Curt Schilling and he had shoulder surgery.”

Mike Harkey, last year’s bullpen coach, Triple-A pitching coach Scott Aldred and Patterson, a former Toronto pitching coach who pitched for the Yankees and was part of their minor league staff before working in the Oakland system this past year, are the leading candidates.